NEW YORK — President Trump swept into this year’s U.N. General Assembly on a positive note, claiming credit during initial meetings Monday that “tremendous progress” has been made in nuclear talks with North Korea and asserting that he intends to hold another face-to-face summit with Kim Jong-un “in the not-too-distant future.”

It was a stark reversal from a year ago, when Mr. Trump made global headlines at the annual gathering of world leaders in New York by deriding Mr. Kim as “Rocket Man” and threatening to “totally destroy” North Korea after a string of provocative missile and weapons tests. This time, Mr. Trump’s aides say, he is poised to capitalize on his unconventional personal diplomacy to forge a new relationship with Pyongyang.

The president may be known for clashing with the United Nations by pulling the U.S. out of its Human Rights Council and the UNESCO cultural program while ending all funding for the U.N. agency for Palestinian refugees. But he moved quickly to seize the initiative of the first day of the General Assembly, known in diplomatspeak as “UNGA,” chairing a panel on combating the global drug crisis and agreeing to a revised bilateral trade agreement with South Korea.

“Last year, we started UNGA and it was trying to figure what the U.S. presence was going to be,” Nikki Haley, U.S. ambassador to the United Nations, told reporters. “This year, we’re here with a bang.”

Secretary of State Mike Pompeo said Mr. Trump intends to use a Tuesday morning speech at the General Assembly to flesh out his “America first” foreign policy, calling on other countries to exert their own “sovereignty to solve challenges” while listening to America’s lead.

Mr. Pompeo said the approach has borne results over the past year, with the administration coordinating international sanctions against Pyongyang while opening the way for direct diplomacy.

“President Trump’s leadership, combined with efforts of countries to enforce the pressure campaign, has de-escalated tensions … and brought us closer to our final goal: the final, fully verified denuclearization” of North Korea.

Uncertainty looms over the extent to which Mr. Kim, who is not attending the U.N. General Assembly, is serious about abandoning his nuclear weapons as promised in his historic summit with Mr. Trump in Singapore in June. U.S. officials hope the prospect of progress overshadows other vexing issues on the table this week in New York.

Rostrum drama

Sparks are expected to fly Tuesday when Iranian President Hassan Rouhani takes to the rostrum shortly after Mr. Trump.

With tensions soaring the over Mr. Trump’s withdrawal from the Obama-era Iran nuclear accord and vow to impose a global embargo on crude oil from Iran by November, Mr. Rouhani is likely to lash out at the president and appeal to U.S. allies that have their own doubts about the Trump administration, analysts say.

Mr. Trump is also expected to go hard. “You can bet the president will have well-deserved strong words for the Iranian regime, which is among the worst of violators of U.N. Security Council resolutions, if not the absolute worst in the world,” Mr. Pompeo said.

But it was the North Korea issue that took center stage Monday as a mob of security swarmed the lavish hallways of the Lotte New York Palace Hotel in midtown Manhattan, where Mr. Trump and his top foreign policy advisers — including Mr. Pompeo, National Security Adviser John R. Bolton and Vice President Mike Pence — met with South Korean President Moon Jae-in.

Last week, Mr. Moon had a three-day summit with Mr. Kim in Pyongyang, where the North Korean leader vowed to consider destroying his main nuclear complex — but only if the U.S. first takes unspecified “corresponding measures.”

Mr. Moon came to New York bearing a personal message from Mr. Kim for Mr. Trump but remained guarded in public remarks on its contents.

Speculation has soared in recent days that Mr. Kim is demanding upfront sanctions relief or a removal of American forces from South Korea as a precondition before taking any concrete measures to reduce its nuclear and ballistic missile arsenals.

Mr. Moon made only broad statements while heaping praise on Mr. Trump. The South Korean president said it was “hugely significant” that Mr. Kim has “expressed his commitment to denuclearization in front of the world media.”

“Chairman Kim also repeatedly conveyed his unwavering trust and expectations for you,” Mr. Moon reported, “while expressing his hope to meet you soon to swiftly conclude the denuclearization process with you, because you are, indeed, the only person who can solve this problem.”

Mr. Trump responded that he sees “tremendous enthusiasm on behalf of Chairman Kim for making a deal” and that “we are in no rush. There’s no hurry.”

The president also said “North Korea has tremendous economic potential.”

“I believe that Chairman Kim and the people of North Korea want to see that potential arrived at,” he said. “And we will help them to that end.”

Peace politics

Mr. Moon, a longtime advocate in South Korea for rapprochement with the North, has said the U.S. president should consider throwing his weight behind a formal declaration officially ending the Korean War, which was frozen 65 years ago by an armistice, as a way to encourage the talks with Pyongyang.

Such a move would be tricky for Washington because it could bring into question the justification for keeping some 30,000 U.S. military personnel positioned in South Korea — a key strategic footprint not far from China.

According to South Korea’s Yonhap News Agency, Mr. Moon has said a formal declaration would be a purely political statement that has nothing to do with U.S. forces on the Korean Peninsula — and that Mr. Kim shares such a view. The South Korean president did not comment on the matter Monday.

Mr. Moon and Mr. Trump also used their bilateral meeting Monday to sign an updated U.S.-South Korea free trade agreement, which Mr. Trump called a “basic redoing” of what had been “a very unfair agreement for the United States.”

Some trade analysts have described the changes to the overhauled treaty as relatively modest, but the White House said in a statement Monday evening that South Korea will double the annual number of American automobiles — from 25,000 to 50,000 per manufacturer per year — that can enter its market using U.S. safety standards rather than more strict South Korean requirements or additional emissions testing.

The agreement also has provisions aimed at expanding U.S. pharmaceutical exports to South Korea and limiting South Korean steel exports to the U.S. South Korea’s National Assembly must approve the deal before it goes into force, and lawmakers have warned that it could face significant opposition if Mr. Trump imposes new tariffs on South Korean car exports.

South Korea’s trade surplus with the U.S. was $ 23 billion last year, down from $ 27.5 billion in 2016. Through the first seven months of 2018, the U.S. bilateral deficit with South Korea was just under $ 10 billion, according to the U.S. government.